scholarly journals Toward design of the antiturbulence surface exhibiting maximum drag reduction effect

2018 ◽  
Vol 850 ◽  
pp. 262-303 ◽  
Author(s):  
V. Krieger ◽  
R. Perić ◽  
J. Jovanović ◽  
H. Lienhart ◽  
A. Delgado
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Stokes Equations ◽  
Flow Direction ◽  
Friction Reduction ◽  
Navier Stokes ◽  
Channel Height ◽  
Initial Flow ◽  
Flat Wall ◽  
Flow Development

The flow development in a groove-modified channel consisting of flat and grooved walls was investigated by direct numerical simulations based on the Navier–Stokes equations at a Reynolds number of $5\times 10^{3}$ based on the full channel height and the bulk velocity. Simulations were performed for highly disturbed initial flow conditions leading to the almost instantaneous appearance of turbulence in channels with flat walls. The surface morphology was designed in the form of profiled grooves aligned with the flow direction and embedded in the wall. Such grooves are presumed to allow development of only the statistically axisymmetric disturbances. In contrast to the rapid production of turbulence along a flat wall, it was found that such development was suppressed over a grooved wall for a remarkably long period of time. Owing to the difference in the flow structure, friction drag over the grooved wall was more than 60 % lower than that over the flat wall. Anisotropy-invariant mapping supports the conclusion, emerging from analytic considerations, that persistence of the laminar regime is due to statistical axisymmetry in the velocity fluctuations. Complementary investigations of turbulent drag reduction in grooved channels demonstrated that promotion of such a state across the entire wetted surface is required to stabilize flow and prevent transition and breakdown to turbulence. To support the results of numerical investigations, measurements in groove-modified channel flow were performed. Comparisons of the pressure differentials measured along flat and groove-modified channels reveal a skin-friction reduction as large as $\text{DR}\approx 50\,\%$ owing to the extended persistence of the laminar flow compared with flow development in a flat channel. These experiments demonstrate that early stabilization of the laminar boundary layer development with a grooved surface promotes drag reduction in a fully turbulent flow with a preserving magnitude as the Reynolds number increases.

scholarly journals Complex singularity analysis for vortex layer flows

2021 ◽  
Vol 932 ◽  
Author(s):  
R.E. Caflisch ◽  
F. Gargano ◽  
M. Sammartino ◽  
V. Sciacca
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Singularity Analysis ◽  
Navier Stokes ◽  
Vortex Sheets ◽  
Initial Flow ◽  
Complex Singularities ◽  
Stagnation Points ◽  
Vortex Layer ◽  
High Reynolds

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier–Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff–Rott singularity seems to suggest that vortex layers, in the limit $Re\rightarrow \infty$ , behave differently from vortex sheets.

scholarly journals Modelling turbulent skin-friction control using linearized Navier–Stokes equations

2012 ◽  
Vol 702 ◽  
pp. 403-414 ◽  
Author(s):  
C. A. Duque-Daza ◽  
M. F. Baig ◽  
D. A. Lockerby ◽  
S. I. Chernyshenko ◽  
C. Davies
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Close Correlation ◽  
Friction Reduction ◽  
Navier Stokes ◽  
Clear Correlation ◽  
Navier Stokes Equations ◽  
The Impact

AbstractLinearized Navier–Stokes equations are solved to investigate the impact on the growth of near-wall turbulent streaks that arises from streamwise-travelling waves of spanwise wall velocity. The percentage change in streak amplification due to the travelling waves, over a range of wave parameters, is compared to published direct numerical simulation (DNS) predictions of turbulent skin-friction reduction; a clear correlation between the two is observed. Linearized simulations at a much higher Reynolds number, more relevant to aerospace applications, produce results that show no marked differences to those obtained at low Reynolds number. It is also observed that there is a close correlation between DNS data of drag reduction and a very simple characteristic of the ‘generalized’ Stokes layer generated by the streamwise-travelling waves.

Turbulent Boundary Layer Control by Wall Oscillations

2005 ◽  
Author(s):  
Dongmei Zhou ◽  
Kenneth S. Ball
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Stokes Equations ◽  
Numerical Data ◽  
Shear Velocity ◽  
Wall Turbulence ◽  
Navier Stokes ◽  
Constant Flow Rate ◽  
Wall Oscillation ◽  
Flow Configurations

The objective of this paper is to examine the effect and the effectiveness of wall oscillation as a control scheme of drag reduction in order to better understand the mechanism of drag reduction. Two flow configurations were considered: constant flow rate and constant mean pressure gradient. The Navier-Stokes equations were solved using Fourier-Chebyshev spectral methods and the oscillation in sinusoidal form was enforced on the walls through boundary conditions for the spanwise velocity component. Results to be shown included the effects of oscillation frequency, amplitude, oscillation orientation, and peak wall speed at Reynolds number of 180 based on wall-shear velocity and channel half-width as well as the Reynolds number dependency s in both flow configurations. Comparison of effectiveness made between these two flow configurations has showed similarities as well as differences. Drag reduction as a function of peak wall speed was compared with both experimental and numerical data and the agreement was good in the trend and in the quantity. Comparison between these two flow configurations in the transient response to the sudden start of wall oscillation, turbulence statistics, and instantaneous flow fields was detailed and differences were clearly shown. Analysis and comparison are allowed to shed some light on the way that oscillations interact with wall turbulence.

System-Level Modeling of Microflows in Circular and Rectangular Channels

2008 ◽  
Author(s):  
Issam A. Lakkis
Keyword(s):  
Reynolds Number ◽  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Direction ◽  
System Level ◽  
Forced Oscillations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
In Series

System-level models for unsteady, incompressible, low Reynolds number flow in channels of slightly varying cross sections of different geometries are presented. The models are based on approximate solution of the unsteady Navier-Stokes equation subject to no-slip and first-order slip boundary conditions. The proposed model, relating the volume rate to the average pressure drop across the channel, is cast into an electric circuit model that consists essentially of an infinite number of parallel branches in series with a resistor and a nonlinear component. The resistor and the nonlinear element in series account respectively for viscous dissipation in the direction of the flow and for the convective part of the inertia term. The set of parallel branches captures the unsteady behavior as well as viscous dissipation normal to flow direction. Previous channel models available in the literature proved to be a special case of the models proposed in this paper at steady state or in the limit of vanishing Reynolds number. The proposed models offer superior accuracy when transient behavior and associated dynamic characteristics are of interest. The models also become more accurate for flows in slightly divergent channels, flows at larger Reynolds number, and in flows that experience sudden changes or that are subjected to forced oscillations with large values of the Strouhal number. The proposed models are flexible in the sense that accuracy and cost can be easily traded by increasing or decreasing the number of branches included in the model. The derived models are compared with previous models and with numerical solutions of the full Navier-Stokes equations.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

On Offset Placement of a Compound Droplet in a Channel Flow

2021 ◽  
Author(s):  
Jagannath Mahato ◽  
Dhananjay Kumar Srivastava ◽  
Dinesh Kumar Chandraker ◽  
Rajaram Lakkaraju
Keyword(s):  
Viscosity Ratio ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Flow Direction ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Lateral Migration ◽  
Navier Stokes Equations ◽  
Deformation Patterns ◽  
Compound Droplet

Abstract Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier-Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Sign in / Sign up

Export Citation Format

Share Document